To unlock the practice Shooting Range you must first successfully beat Mission mode.

Unlock Billy Ray Logg:
Defeat him in mission mode with any character

Unlock Mousey McNuts:
Defeat him in mission mode with any character

Unlock Professor Von Brown:
Defeat him in mission mode with any character

Unlock ISO-7982:
Complete mission mode

Complete the following tasks to unlock the corresponding achievements and their alloted GamerScore.

Six Degrees of Small Arms - GamerScore 0:
Play online against someone who already has the achievement to get it.

Challenge x15 - GamerScore 10:
In Challenge mode defeat 15 opponents.

Won 10 Matches - GamerScore 10:
Win 10 matches in Single Player mode or by playing on Xbox Live.

Completed Training - GamerScore 10:
Using any character complete the Single Player Training mode.

Won 50 Matches - GamerScore 15:
Win 50 matches in Single Player mode or by playing on Xbox Live.

Combo x2 - GamerScore 15:
Kill 2 opponents in rapid succession

Combo x5 - GamerScore 20:
Kill 5 opponents in rapid succession

Challenge x50 - GamerScore 20:
In Challenge mode defeat 50 opponents.

Complete Mission Mode - GamerScore 20:
Complete mission mode.

Marksmanship - GamerScore 25:
In the 'Shooting Range' score over 10,000.

Played 100 Matches - GamerScore 25:
Either offline or on Xbox Live play 100 matches.

Won 100 Matches - GamerScore 25:
In Mission mode or Battle mode win 100 matches